Problem: Express this product in scientific notation: $(8.50\times 10^{-2})\times (7.00\times 10^{-1})$
Start by collecting like terms together. $= (8.50\times 7.00) \times (10^{-2}\times 10^{-1})$ When multiplying exponents with the same base, add the powers together. $= 59.5 \times 10^{-2\,+\,-1}$ $= 59.5 \times 10^{-3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $59.5$ is the same as $5.950 \times 10$ $ = {5.950 \times 10} \times 10^{-3} $ $= 5.950\times 10^{-2}$